Let G be a finite group. In order to determine the smallest cardinality d (G) of a generating set
of G and a generating set with this cardinality, one should repeat 'many times' the test …

arXiv:2404.03952v1 [math.GR] 5 Apr 2024 Minimal sized generating sets of permutation groups
Page 1 arXiv:2404.03952v1 [math.GR] 5 Apr 2024 Minimal sized generating sets of permutation …

By now, we have a product theorem in every finite simple group G of Lie type, with the
strength of the bound depending only in the rank of G. Such theorems have numerous …

In 1993, Praeger introduced quasiprimitive permutation groups. A finite group acting on a
finite set is said to act quasiprimitively if every non-trivial normal subgroup acts transitively. In …

In this paper, we study finite semiprimitive permutation groups, that is, groups in which each
normal subgroup is transitive or semiregular. These groups have recently been investigated …

We obtain an asymptotic upper bound for the product of the p-parts of the orders of certain
composition factors of a finite group acting completely reducibly and faithfully on a finite …

We denote the smallest size of a generating set of a group G by d (G). We prove that d (G)
log⁡| G|= O (n 2 log⁡ q) for irreducible subgroups G of GL (n, q), and estimate the …

Let T be a finite simple group. For a finite group G, we determine an upper bound on the
number cT (G) of composition factors of G that are isomorphic to T. We consider this problem …

A subexponential bound on the cardinality of abelian quotients in finite transitive groups -
Lucchini - 2021 - Bulletin of the London Mathematical Society - Wiley Online Library Skip to …